{
  "id": "1204.2074",
  "version": "v2",
  "published": "2012-04-10T08:09:56.000Z",
  "updated": "2013-06-20T01:31:17.000Z",
  "title": "Weak convergence of self-normalized partial sums processes",
  "authors": [
    "Miklós Csörgő",
    "Zhishui Hu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\{X, X_n, n\\geq 1\\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \\sum^n_{i=1} X_i$ and $V_n^2=\\sum^n_{i=1} X_i^2, n\\ge 1.$ A weak convergence theorem is established for the self-normalized partial sums processes $\\{S_{[nt]}/V_n, 0\\le t\\le 1\\}$ when $X$ belongs to the domain of attraction of a stable law with index $\\alpha \\in (0,2]$. The respective limiting distributions of the random variables ${\\max_{1\\le i\\le n}|X_i|}/{S_n}$ and ${\\max_{1\\le i\\le n}|X_i|}/{V_n}$ are also obtained under the same condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-20T01:31:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "60G52"
    ],
    "keywords": [
      "self-normalized partial sums processes",
      "weak convergence",
      "distributed non-degenerate random variables",
      "independent identically distributed non-degenerate random"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2074C"
    }
  }
}